Analysis and Control of Age-Dependent Population Dynamics / Edition 1

by S. Anita

Overview

The material of the present book is an extension of a graduate course given by the author at the University "Al.I. Cuza" Iasi and is intended for students and researchers interested in the applications of optimal control and in mathematical biology. Age is one of the most important parameters in the evolution of a bi­ ological population. Even if for a very long period age structure has been considered only in demography, nowadays it is fundamental in epidemiology and ecology too. This is the first book devoted to the control of continuous age structured populationdynamics.It focuses on the basic properties of the solutions and on the control of age structured population dynamics with or without diffusion. The main goal of this work is to familiarize the reader with the most important problems, approaches and results in the mathematical theory of age-dependent models. Special attention is given to optimal harvesting and to exact controllability problems, which are very important from the econom­ ical or ecological points of view. We use some new concepts and techniques in modern control theory such as Clarke's generalized gradient, Ekeland's variational principle, and Carleman estimates. The methods and techniques we use can be applied to other control problems.

Product Details

ISBN-13:	9780792366393
Publisher:	Springer Netherlands
Publication date:	10/31/2000
Series:	Mathematical Modelling: Theory and Applications , #11
Edition description:	2000
Pages:	201
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1 Introduction.- 2 Analysis of Age-Dependent Population Dynamics.- 3 Optimal Control of Population Dynamics.- 4 Analysis of Population Dynamics with Diffusion.- 5 Control of Population Dynamics with Diffusion.- Appendix 1: Elements of Nonlinear Analysis.- A1.1 Convex functions and subdifferentials.- A1.2 Generalized gradients of locally Lipschitz functions.- A1.3 The Ekeland variational principle.- Appendix 2: The Linear Heat Equation.- References.